Value Sharing Results for Generalized Shifts of Entire Functions

Jump To References Section

Authors

  • Goutam Haldar
     Department of Mathematics, Malda College, Malda - 732101 West Bengal ,IN

DOI:

https://doi.org/10.18311/jims/2023/27445

Keywords:

Meromorphic Function, Entire Function, Shift Operator, Small Function, Weakly Weighted Sharing, Relaxed Weighted Sharing.
30D35

Abstract

In this paper, we investigate the uniqueness problem of generalized shift polynomials of finite order entire functions sharing a small function under the notion of weakly and relaxed weighted sharing environment. Some examples have been exhibited which are relevant to the content of the paper.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2023-03-24

How to Cite

Haldar, G. (2023). Value Sharing Results for Generalized Shifts of Entire Functions. The Journal of the Indian Mathematical Society, 90(1-2), 53–66. https://doi.org/10.18311/jims/2023/27445

Issue

Volume 90, Issue 1-2, January-June 2023

Section

Articles

License

Copyright (c) 2023 Goutam Haldar

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC
Received 2021-03-28
Accepted 2022-05-25
Published 2023-03-24

 

References

A. Banerjee and S. Mukherjee, Uniqueness of meromorphic functions concerning differential monomials sharing the same value, Bull. Math. Soc. Sci. Math. Roum. Nouv. Ser., 50 (2007), 191 – 206.

W. Bergweiler and J. K. Langley, Zeros of difference of meromorphic functions, Math. Proc. Camb. Philos Soc., 142 (2007), 133 – 147. DOI: https://doi.org/10.1017/S0305004106009777

Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane, Ramanujan J., 16 (2008), 105 – 129. DOI: https://doi.org/10.1007/s11139-007-9101-1

C. Y. Fang and M. L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 44 (2002), 607 – 617. DOI: https://doi.org/10.1016/S0898-1221(02)00175-X

R. G. Halburdand and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 31(2) (2006), 463 – 478.

W. K. Hayman, Picard values of meromorphic Functions and their derivatives, Ann. Math., 70 (1959), 9 – 42. DOI: https://doi.org/10.2307/1969890

W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.

J. Heittokangas, J., R. Korhonen, I. Laine, J. Rieppo and J. L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl., 355 (2009), 352 – 363. DOI: https://doi.org/10.1016/j.jmaa.2009.01.053

I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28 (2001), 83 – 91. DOI: https://doi.org/10.1155/S0161171201011036

I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241 – 253. DOI: https://doi.org/10.1080/17476930108815411

S. H. Lin and W. C. Lin, Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai Math. J., 29 (2006), 269 – 280. DOI: https://doi.org/10.2996/kmj/1151936441

X. Q. Lin and W. C. Lin, Uniqueness of entire functions sharing one value, Acta Math. Sci., Ser. B. Engl. Ed., 31 (2011), 1062 – 1076. DOI: https://doi.org/10.1016/S0252-9602(11)60298-1

X. Luo and W. C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl., 377 (2011), 441 – 449. DOI: https://doi.org/10.1016/j.jmaa.2010.10.055

C. Meng, Uniqueness of entire functions concerning difference polynomials, Math. Bohem., 139 (2014), 89 – 97. DOI: https://doi.org/10.21136/MB.2014.143638

P. Sahoo, Uniqueness of Entire Functions Related to Difference Polynomials, Commun. Math. Stat., 3 (2015), 227 – 238. DOI: https://doi.org/10.1007/s40304-015-0057-y

C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107 – 112. DOI: https://doi.org/10.1007/BF01110921

C. C. Yang and X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math., 22 (1997), 395 – 406.

H. X. Yi, Meromorphic functions that share one or two values, Complex Var. Theory Appl., 28 (1995), 1 – 11. DOI: https://doi.org/10.1080/17476939508814833

J. L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367 (2010), 401 – 408. DOI: https://doi.org/10.1016/j.jmaa.2010.01.038